A method for evaluating the process capability index of CNC machining parts

Abstract

The present invention relates to the field of CNC machining, and specifically to a method for evaluating the process capability index of CNC machining parts, comprising the following steps: a first step: constructing a skew-normal process capability index of a position-scale distribution; a second step: replacing any quantile with a quantile of a standardized distribution; a third step: calculating the process capability index of a skew-normal distribution; and a fourth step: evaluating the process capability index. The present invention proposes a robust non-normal process capability index. This new index has a reasonable construction principle and a simple structure, can remain robust to changes in skewness, is easy to calculate, has a unified dimension, and can effectively evaluate the capability of a production process. The index not only covers the existing mainstream process capability index forms, but is also applicable to all position-scale family distributions, or distribution types that can be converted into this distribution family.

Description

Technical Field

[0001] The invention relates to the technical field of numerical control machining, in particular to an evaluation method for the process capability index of numerical control machining parts. Background Art

[0002] Once the production process is under control, the core goal of product quality management is to ensure that products meet specifications through a stable and consistent production process. Therefore, after confirming that the production process is under control, it is necessary to assess whether the products meet quality standards. If substandard products are found, improvement directions should be provided. To address this issue, the process capability index has become a key assessment and analysis tool.

[0003] During CNC machining, the primary concern is ensuring that fluctuations in the quality characteristic values ​​of machined parts remain within a controllable range. However, even when this condition is met, deviations from the normal distribution assumption often occur. For example, if CNC machine operators harbor subjective biases, this can cause the manufacturing process to deviate from a normal distribution. For example, when machining nuts of a certain specification, operators often tend to produce slightly larger products. This is because larger products can be reworked and repaired if they fail, while smaller products cannot be repaired and must be scrapped. This phenomenon is common in the parts machining industry. Furthermore, tool wear and measurement tool datum errors during machining can also cause systematic drift and deviation in part quality characteristic values.

[0004] With the continuous improvement of production technology and product quality requirements, the challenges faced by producers are becoming more complex. The normality assumption of product quality characteristics is gradually no longer applicable in some areas. Many scholars have discussed this issue and believe that the data involved in quality control management often do not conform to the normal assumption, and may even be asymmetric. According to the normal assumption, the distribution is symmetrical, so the expected value and the median are equal; but in the case of asymmetric distribution, this conclusion no longer holds. If the process capability index is still calculated according to the normal distribution, incorrect conclusions may be drawn. English and Taylor's research analyzed two commonly used process capability indices - C p and C pk , and explored their robustness when the random process deviates from normality. The results show that these two indices lack robustness when the data is non-normal, especially C pk Therefore, the researchers recommend that the actual situation of the process distribution should be considered before using the conventional normal process capability index.

[0005] To address this issue, many scholars have adopted different methods to study the non-normal process capability index, among which the most common ones include: quantile method and data conversion method.

[0006] Clements constructed a non-normal distribution process capability index based on the quantiles of the distribution. The calculation method is as follows:

[0007] Among them, L1, L2 and L3 are the 0.135%, 50% and 99.865% quantiles of the distribution respectively. There are some problems in the application of the quantile method. The first is the interpretability of the index and the robustness to skewness. In practice, the Clements method based on quantiles cannot effectively distinguish whether product quality failures are caused by median shift or variance changes, resulting in the inability to provide managers with specific process improvement directions, and therefore lacks practical interpretability. In addition, the quantile method is very sensitive to distribution skewness when estimating non-normal process capability indices. When the sample size is small and the skewness is large, this method cannot provide accurate estimates, resulting in errors in practical applications. Research by Martin and Libor shows that when the probability distribution of process characteristics is non-normal, the C calculated using traditional methods p and C pk Indices often lead to incorrect interpretations of process capability, which also limits the scope of use of quantile methods.

[0008] Process capability indices can also be calculated by converting non-normal data to a normal distribution. This method of converting data to normal data is widely used in statistics and other fields. Rivera et al. proposed converting process output data to normally distributed data using a function and calculating their process capability indices using traditional methods. However, the applicability of numerical conversion methods is also limited. Not all non-normal data can be converted to a normal distribution through data conversion, which significantly limits practical applications. Data conversion methods not only require processing large amounts of data but also involve cumbersome calculations. The converted data must undergo repeated normality tests, resulting in complex calculations. The conversion coefficients are estimated, which inevitably leads to errors. Furthermore, some information in the original data is lost during the conversion process, resulting in discrepancies between the calculated process capability index and the actual process capability. Summary of the Invention

[0009] To achieve the above objectives, the present invention proposes a robust non-normal process capability index. This new index has a reasonable construction principle and a simple structure, can remain robust to skewness changes, is easy to calculate, has a unified dimension, and can effectively evaluate the production process capability. This index not only covers the existing mainstream process capability index forms (such as C p ,C pk ,C pm ,C pmk ), and is also applicable to all position-scale family distributions, or distribution types that can be converted into this distribution family. The present invention provides the following technical solutions:

[0010] A method for evaluating the process capability index of CNC machining parts, comprising:

[0011] Step 1: Construction of skew normal process capability index of location-scale distribution;

[0012] Step 2: Use the quantile of the standardized distribution to replace any quantile;

[0013] Step 3: Calculate the process capability index of the skew normal distribution;

[0014] Step 4: Process capability index evaluation.

[0015] As a further solution of the present invention: the construction of the skew normal process capability index of the location-scale distribution is specifically as follows: the present invention assumes that the random variable Y obeys the location parameter ζ and the scale parameter ω 2 The skewed normal distribution, that is, Y SN ~SN(ζ,ω 2 ). Its distribution function is in is the distribution function of the standardized location-scale distribution. According to the properties of the location-scale function, any quantile α can be expressed as: Q α SN =ζ+ωG SN -1 (α)(1).

[0016] As a further solution of the present invention, using the quantile of the standardized distribution to replace any quantile is specifically: the distance between any quantile α1 of the position-scale distribution and another quantile α2 can be expressed by the standard deviation and the quantile difference of the standardized distribution:

[0017]

[0018] In formula (2), G SN -1 (α2)-G SN -1(α1) is a constant, which means that for the location-scale distribution, the distance between its quantiles can be expressed as a constant multiple of the standard deviation. Based on this property, we can improve the process capability index of the Clements method and obtain a new skewed normal process capability index. This new non-normal process capability index not only retains the advantages of the Clements method, but also is a function of the median and standard deviation. Therefore, it can not only evaluate process capability, but also propose a set of process capability improvement plans based on the median and standard deviation when the process capability is insufficient. In addition, the location-scale distribution has an important statistical property: the skewness of its distribution is constant and does not change with changes in parameters. Based on this property, a robust process capability index can be further constructed.

[0019] As a further solution of the present invention: the process capability index of the skew normal distribution is calculated as follows: According to formula (2), ω·(G SN -1 (α2)-G SN -1 (α1)) instead of X in Clements' method 0.99865 -X 0.00135 , we can get the process capability index C of skew normal distribution p SN :

[0020]

[0021] In formula (3), G SN - 1 (0.99865)-G SN - 1 (0.00135) is a constant. When the data is normally distributed, G SN -1 (0.99865)-G SN -1 (0.00135) = 6, C p SN Equal to C p It is not difficult to see that, like the normal process capability index, as the scale parameter increases, the skew normal process capability index decreases. In the case where the distribution center and the tolerance center are offset, it is necessary to calculate the corrected process capability index C pk . Use ω·(G SN -1 (0.99865)-G SN -1 (0.5)) and ω·(G SN -1 (0.5)-G SN -1(0.00135)) instead of X in the Clements method 0.99865 -X 0.5 and X 0.5 -X 0.00135 , so that this index can well explain the asymmetric tolerance of asymmetric distribution, and can find the improvement strategy of process capability based on the median and standard deviation. pk SN The calculation formula is:

[0022]

[0023] In order to consider the target value T set in machining, the process capability index C is introduced pm 、C pmk , C pm The calculation formula can be expressed in the following form:

[0024]

[0025] Where, X 0.99865 and X 0.00135 Represent the 99.865% and 0.135% quantiles on both sides of the normal distribution function. In the skew normal distribution, according to the location-scale distribution function calculation method proposed in this paper, ω·(G SN -1 (α2)-G SN -1 (α1)) instead of X 0.99865 -X 0.00135 , using the median Q 0.5 SN Instead of the mean μ, the skew normal distribution process capability index C can be obtained pm SN The calculation formula is:

[0026]

[0027] Skewed normal distribution process capability index C pmk SN The calculation formula is:

[0028]

[0029] As a further solution of the present invention: Process capability index evaluation is specifically: comparing the process capability index with a preset threshold value to determine the process capability level. p ,C pk ,C pm ,C pmk) ≥ 1.67, indicating very high process capability. In this case, neither intermediate nor final part testing is required, as the entire machining process is stable and reliable, with virtually no risk of out-of-tolerance deviations. When 1.67 > 1.33 ≥ 1.33, the process capability is relatively sufficient, and intermediate part testing can be omitted. However, final part testing is still required to ensure that critical dimensions meet design requirements. When 1.33 > 1.0 ≥ 1.0, the process capability is fair, and intermediate and final part testing is necessary. Inspecting intermediate parts allows for timely detection of deviations, allowing tool paths to be adjusted to ensure final dimensions meet tolerances. When 1.0 > 0.67 ≥ 0.67, the process capability is insufficient, requiring rigorous testing of intermediate and final parts. By analyzing intermediate parts, the cause of the insufficient process capability can be identified, allowing optimization of the machining process or adjustment of the part design. When the process capability index is < 0.67, the process capability is severely insufficient, requiring an immediate and comprehensive inspection, possibly even downtime or improvement, to ensure that the production process meets required standards.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] The skew-normal distribution process capability index proposed in the present invention has important practical application value, especially in solving the problem of skewness robustness. By utilizing the statistical properties of the location-scale family distribution, the present invention effectively solves the problem of parameter robustness in theory. Unlike traditional indices, the skew-normal process capability index of the present invention has a unified dimension between different indices and can accurately reflect the process capability. As in the case of normal distribution, the above four skew-normal process capability indices will produce the same numerical value under the same parameters and conditions, ensuring the consistency and reliability of their calculation results. In addition, the process capability index has a wide range of applications. The previous skew-normal process capability index is usually only applicable to a specific type of distribution, while the index proposed in the present invention is applicable to all location-scale distributions, and can even be extended to other distribution types that can be converted into location-scale distributions. When the data conforms to the normal distribution, the process capability index will degenerate into the traditional process capability index, ensuring its applicability and flexibility under different distributions. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 Flowchart of a method for evaluating the process capability index of CNC machining parts in an embodiment of the present invention.

[0033] Figure 2 50 groups of component inspection data histograms in an embodiment of the present invention.

[0034] Figure 3: This is a probability density diagram of the detection data of 50 groups of parts in an embodiment of the present invention.

[0035] Figure 4 This is a quality control diagram in an embodiment of the present invention.

[0036] Figure 5 This is a flow chart of the skew normal distribution process capability evaluation strategy in an embodiment of the present invention.

[0037] Figure 6 Schematic diagram of normal distribution and skewed normal distribution in an embodiment of the present invention. DETAILED DESCRIPTION

[0038] The following will provide a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0039] Many automated manufacturing companies use process capability indices to measure whether the manufacturing process's capabilities meet quality requirements. In practical production, we must first ensure that the volatility of the output quality characteristic values ​​of the production process is within a controllable range. Even so, the normal distribution assumption is often not met. To address this issue, the present invention proposes a skewed normal process capability index assessment method based on the position-scale distribution, building on the quantile method. This method is less affected by distribution skewness and provides more reliable theoretical support for the evaluation and improvement of process capability.

[0040] The specific implementation of the present invention is described in detail below with reference to specific embodiments.

[0041] Example 1, see Figures 1-6 This example is the data from a machine tool company processing a certain component. A total of 50 sets of measurement data were collected (see Table 1). The data histogram is as follows: Figure 2 As shown, the probability density diagram is Figure 3 shown.

[0042] Table 1 50 sets of parts inspection data

[0043] 29.1 29.2 29.3 29.4 29.4 29.4 29.4 29.5 29.5 29.5 29.6 29.6 29.6 29.6 29.7 29.7 29.7 29.7 29.7 29.8 29.8 29.8 29.8 29.8 29.8 29.8 29.9 29.9 29.9 29.9 29.9 30.0 30.0 30.0 30.0 30.0 30.1 30.1 30.1 30.2 30.2 30.2 30.3 30.3 30.4 30.4 30.6 30.6 30.8 30.9

[0044] from Figure 2 As can be seen from the data histogram, this data set does not follow a normal distribution. Therefore, we will evaluate process capability based on the nonnormal process capability analysis strategy proposed in this invention. According to the customer's requirements, the ULS, LSL, and target values ​​are 31.0, 29.0, and 30.0, respectively.

[0045] A quality control chart is a tool used to monitor and analyze process variation by plotting changes in process data, such as Figure 4 , helping us identify abnormal fluctuations, trends, deviations and instabilities in the process, by Figure 4 The quality control chart shows that the process is in a controlled state.

[0046] from Figure 2 The data histogram can preliminarily determine whether the data may obey the Weibull distribution or the log-logistic distribution. Through maximum likelihood estimation and KS test, it is verified that this group of data obeys the log-logistic distribution with a shape parameter of 13.08 and a size parameter of 24.42.

[0047] Figure 5 This is the flow chart of the skew normal distribution process capability evaluation strategy. Figure 6 is a schematic diagram of normal distribution and skew normal distribution, from Figure 5 It can be seen from the figure that the process capability index constructed according to the skewed normal distribution of the present invention requires that the data be first transformed into a logistic distribution of the location-scale family distribution. The logarithm of the original data, target value, and upper and lower specification limits is taken, and then the process capability index C is obtained according to the process capability index calculation method given in this article. p SN , C pk SN , C pm SN , C pmk SN They are 0.93, 0.90, 0.93, and 0.92 respectively. According to the process capability index evaluation method, it is believed that the process capability of this CNC machine tool is insufficient. The cause of the large fluctuation in processing level should be found, and the intermediate and final states of the parts should be strictly tested.

[0048] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A method for evaluating the process capability index of CNC machining parts, characterized in that: The following steps are involved: Step 1: Construction of the skew normal process capability index of the location-scale distribution. The construction of the skew normal process capability index of the location-scale distribution is specifically as follows: the random variable Y obeys the location parameter ζ and the scale parameter ω 2 The skewed normal distribution, that is, Y SN ~SN(ζ,ω 2 ), and its distribution function is in is the distribution function of the standardized location-scale distribution. According to the properties of the location-scale function, any quantile α is expressed as: Q α SN =ζ+ωG SN -1 (α)(1); Step 2: Use the quantile of the standardized distribution to replace any quantile. The specific method of using the quantile of the standardized distribution to replace any quantile is: the distance between any quantile α1 of the location-scale distribution and another quantile α2 is expressed as the standard deviation and the quantile difference of the standardized distribution: In formula (2), G SN -1 (α2)-G SN -1 (α1) is a constant; Step 3: Calculate the process capability index of the skew normal distribution. The specific calculation of the process capability index of the skew normal distribution is as follows: According to formula (2), use ω·(G SN -1 (α2)-G SN -1 (α1)) instead of X in Clements' method 0.99865 -X 0.00135 , and obtain the process capability index C of the skew normal distribution p SN : In formula (3), G SN -1 (0.99865)-G SN -1 (0.00135) is a constant. When the data is normally distributed, G SN -1 (0.99865)-G SN -1 (0.00135) = 6, C p SN Equal to C p ; Step 4: Process capability index evaluation.

2. The method for evaluating the process capability index of CNC machining parts according to claim 1, characterized in that: Also calculate the modified process capability index C pk , skew normal distribution process capability index C pk SN The calculation formula is:

3. The method for evaluating the process capability index of CNC machining parts according to claim 2, characterized in that: Also calculate the process capability index C pm 、C pmk , C pm The calculation formula is expressed in the following form: Where, X 0.99865 and X 0.00135 Represents the 99.865% and 0.135% quantiles on both sides of the normal distribution function, respectively, and the skew normal distribution process capability index C pm SN The calculation formula is: Skewed normal distribution process capability index C pmk SN The calculation formula is:

4. The method for evaluating the process capability index of CNC machining parts according to claim 3, characterized in that: The process capability index evaluation specifically includes: comparing the process capability index with a preset threshold value to determine the process capability level.

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